1. Field of the Invention
The present invention is in the field of atmospheric turbulence, and in particular, relates to an optical apparatus designed to provide in-situ estimates of the Rytov parameter for the propagation of light through atmospheric optical turbulence.
2. Description of the Prior Art
The term xe2x80x9cRytov parameterxe2x80x9d refers to the theoretical log-amplitude variance predicted by Rytov theory. The Rytov parameter for spherical-wave propagation is given as a weighted integral of the random index-of-refraction structure constant Cn2 as follows:                               σ          x          2                ≡                  0.5631          ⁢                      xe2x80x83                    ⁢                                    (                                                2                  ⁢                                      xe2x80x83                                    ⁢                  π                                λ                            )                                      7              /              6                                ⁢                      xe2x80x83                    ⁢                                    ∫              0              L                        ⁢                          xe2x80x83                        ⁢                                          ⅆ                z                            ⁢                              xe2x80x83                            ⁢                              C                n                2                            ⁢                              xe2x80x83                            ⁢                                                                    (                    z                    )                                    ⁢                                      xe2x80x83                                    [                                      z                    ⁢                                          xe2x80x83                                        ⁢                                          (                                              1                        -                                                  z                          /                          L                                                                    )                                                        ]                                                  5                  /                  6                                                                                        (        1        )            
where xcex is the wavelength, L is the propagation distance, and z is a position along the propagation path. Though strictly a theoretical quantity, the Rytov parameter is a useful metric of the optical effects for extended-turbulence propagation and is a leading indicator of the performance limitations of adaptive-optical compensation devices not related to the transverse coherence diameter (Fried parameter) (D. L. Fried, xe2x80x9cOptical resolution through a randomly inhomogeneous medium for very long and very short exposures,xe2x80x9d J. Opt. Soc. Am. 56, pp. 1372-1379, October 1966). This instrument bases the estimate of the Rytov parameter on an appropriate difference of variances for the differential image motion (average wave-front gradient, wave-front tilt) between two receiving apertures. The use of differential tilts for determining the Rytov parameter is a primary novel aspect of this invention, for these quantities are not conventionally recognized to be indicative of the Rytov parameter. When interpreted properly, differential-tilt measurements are a reliable and predictable indicator of the Rytov parameter. It is important to clarify that the differential-tilt Rytov parameter monitor is used to estimate the value of the integral expression for "sgr""khgr"2 given in Eq. (1), not the observed log-amplitude variance for point-source propagation.
The Rytov approximation is the predominant theoretical construct used to derive a solution to the scalar wave equation for propagation through a medium with random index-of-refraction fluctuations. Analysis of turbulence effects using the Rytov approximation is often referred to as xe2x80x9cRytov theory.xe2x80x9d The variance of the log-amplitude computed using Rytov theory is called the xe2x80x9cRytov parameter.xe2x80x9d This quantity is designated "sgr""khgr"2 is related to point source propagation parameters as indicated in Eq. (1). While Eq. (1) indicates that "sgr""khgr"2 should increase proportionately with any constant multiplier of Cn2, experimental and simulation-based studies have concluded that this trend does not hold for full-wave propagation. Instead, the irradiance variance (scintillation) increases monotonically from 0 to a maximum value greater than 1, then decreases as Cn2 increases. This behavior is referred to as the xe2x80x9csaturationxe2x80x9d of scintillation. Saturation imposes a limit on the utility of irradiance-based instrumentation (scintillometers) to adz accurately determine turbulence strength parameters using Rytov theory. In many experiments, the Rytov parameter cannot be measured directly, but rather must be inferred from measurable quantities making key assumptions about the turbulence profile that are not generally valid.
The Rytov parameter is often used to quantify the severity of turbulence effects in propagation, especially in studies of scintillation. Moreover, the Rytov parameter is a critical metric in determining the utility of adaptive-optical systems for compensation of extended-turbulence effects. Recently, it has been recognized that the Rytov parameter is related to a rotational component of the turbulence-induced phase due to phase dislocations (branch points) which limit the ability of conventional wave-front reconstruction procedures (D. L. Fried, xe2x80x9cBranch point problem in adaptive optics,xe2x80x9d J. Opt. Soc. Am. A 15, pp. 2759-2768, October 1998). The Rytov parameter addresses additional adaptive optics performance degradation not quantified by considering only the transverse atmospheric coherence length r0 or Fried parameter. Thus, it is desirable to accurately estimate the Rytov parameter in field experiments where little or nothing is known about Cn2(z). For simulation studies, the Rytov parameter may be computed directly from the input parameters. An accurate estimate of the Rytov parameter in practical experiments therefore facilitates comparison with simulation-based studies.
In current laser propagation and adaptive-optical compensation field tests, at least two types of atmospheric characterization measurements are typically made. The first type of measurement relates to the variation of the received irradiance or scintillation. This measurement is made with a device called a scintillometer, which measures the random fluctuation of received light in a collection aperture. Devices of this type have been patented by Hill and Ochs (U.S. Pat. No. 5,150,171, Thierman (U.S. Pat. No. 5,303,024), and Wang (U.S. Pat. No. 5,796,105). For conventional scintillometers, the irradiance variance is computed from the data and analysis is performed to yield an estimate of Cn2. Since these measurements are typically made over nearly horizontal paths, it is assumed that Cn2 varies little over the path. The observed irradiance variance may be interpreted using Rytov theory in the weak-fluctuations regime, or a comparison with wave-optics simulation results may be made in the saturated or asymptotic regimes. From the estimate of Cn2 obtained with the scintillometer, the Rytov parameter may then be computed using Eq. (1).
The second type of atmospheric characterization measurement often made in field tests relates to the strength of the turbulence-induced phase, quantified by the transverse coherence length r0 which is related to point-source propagation parameters as follows:                               r          0                ≡                              (                          [                                                2.91                  6.88                                ⁢                                  xe2x80x83                                ⁢                                                      (                                                                  2                        ⁢                                                  xe2x80x83                                                ⁢                        π                                            λ                                        )                                    2                                ⁢                                  xe2x80x83                                ⁢                                                      ∫                    0                    L                                    ⁢                                      xe2x80x83                                    ⁢                                                            ⅆ                      z                                        ⁢                                          xe2x80x83                                        ⁢                                          C                      n                      2                                        ⁢                                          xe2x80x83                                        ⁢                                          (                      z                      )                                        ⁢                                          xe2x80x83                                        ⁢                                                                  (                                                  1                          -                                                      z                            /                            L                                                                          )                                                                    5                        /                        3                                                                                                        ]                        )                                              -              3                        /            5                                              (        2        )            
A mathematical comparison between Eq. (1) for "sgr""khgr"2 and Eq. (2) for r0 indicates that while the bulk of the contribution to "sgr""khgr"2 comes from the middle of the propagation path, r0 is affected primarily by turbulence near the receive aperture. Thus, "sgr""khgr"2 and r0 are indicative of disparate optical effects arising from different regions of the propagation path. For an optical system with diameter D, atmospheric effects on resolution are determined by the quantity (D/r0)5/3. A device for measuring r0 has been patented by Wilkins (U.S. Pat. No. 5,343,287) that employs beam-spread and angle-of-arrival variance. However, work dating back more than 20 years (D. L. Fried, xe2x80x9cDifferential angle of arrival: Theory, evaluation, and measurement feasibility,xe2x80x9d Radio Science 10, pp. 71-76, January 1975; F. D. Eaton, et al., xe2x80x9cComparison of two techniques for determining atmospheric seeing,xe2x80x9d in Proc. SPIE: Optical, Infrared, and Millimeter Wave Propagation Engineering, vol. 926, pp. 319-334, 1988; and F. D. Eaton, et al., xe2x80x9cPhase structure function measurements with multiple apertures,xe2x80x9d in Proc. SPIE: Propagation Engineering, vol. 1115, pp. 218-223, 1989) demonstrates the superiority of techniques employing differential angle-of-arrival measurements of two spatially-separated receive apertures for estimating r0.
In cases where Cn2 may reasonably be assumed constant over the entire propagation path, either irradiance variance measurements from a scintillometer or r0 measurements from a suitable device could be used to compute Cn2 from Rytov theory or simulation, and the Rytov parameter could then be computed using Eq. (1). In practice, however, constant Cn2 is rarely observed over a propagation distance greater than several hundred meters. Thus, neither the irradiance-based (scintillometer) nor conventional phase-variance-based techniques provide a reliable method for determining the Rytov parameter. Additionally, analysis of scintillometer data using wave-optics simulations may require a measurement of the inner scale of turbulence for enhanced fidelity. Taken together, limitations of the available devices and techniques for atmospheric characterization may lead to large errors in estimating the Rytov parameter for realistic turbulence profiles.
The differential-tilt Rytov parameter monitor is an optical apparatus, which when combined with related processing and data analysis techniques, provides in-situ estimates of the theoretical expression of the Rytov parameter for point source propagation of light through atmospheric optical turbulence. The Rytov parameter is the theoretical log-amplitude variance predicted by Rytov theory. It is a useful metric of the optical effects for extended turbulence propagation and is a leading indicator of the performance limitations of adaptive optical compensation devices not related to the transverse coherence diameter (Fried parameter). The present invention bases the estimate of the Rytov parameter on an appropriate difference of variances for the differential image motion (average wavefront gradient and wavefront tilt) between two receiving apertures, quantities that are not conventionally recognized to be indicative of the Rytov parameter. A time-duplex alternative apparatus and a single source alternative apparatus are also disclosed.